This study will explore the possible effectiveness of levetiracetam in patients with bipolar illness who have not responded adequately to standard treatments. Levetiracetam was recently approved to treat seizures. Other drugs in the same class as levetiracetam, including carbamazepine and valproate, are widely recognized as substitute medications for lithium or are used as an adjunct to it, and other anticonvulsants have also shown promise in improving bipolar symptoms.